A Review on the Performance of Linear and Mixed Integer Two-Stage Stochastic Programming Software

This paper presents a tutorial on the state-of-the-art software for the solution of two-stage (mixed-integer) linear stochastic programs and provides a list of software designed for this purpose. The methodologies are classified according to the decomposition alternatives and the types of the variables in the problem. We review the fundamentals of Benders decomposition, dual decomposition and progressive hedging, as well as possible improvements and variants. We also present extensive numerical results to underline the properties and performance of each algorithm using software implementations, including DECIS, FORTSP, PySP, and DSP. Finally, we discuss the strengths and weaknesses of each methodology and propose future research directions.

Automated summary

This paper presents a tutorial on state-of-the-art software for solving two-stage (mixed-integer) linear stochastic programs and provides a list of software designed for this purpose. It classifies the methodologies based on decomposition alternatives and variable types. The paper reviews the fundamentals of Benders decomposition, dual decomposition, and progressive hedging, along with possible improvements and variants. It also presents extensive numerical results to showcase the properties and performance of each algorithm using various software implementations, including DECIS, FORTSP, PySP, and DSP. Finally, it discusses the strengths and weaknesses of each methodology and proposes future research directions.